Modulating flow and heat transfer through the competition of electroosmotic and electromagnetic driving forces

This study investigates flow and heat transfer in a parallel-plate microchannel containing a Powell–Eyring fluid under a constant pressure gradient such that electroosmotic and electromagnetic forces compete to govern transport behavior. The incorporation of the slip boundary conditions enables a coupled mathematical framework to capture the effects of non-Newtonian rheology, electromagnetic body forces, and heat transport. The governing equations are treated using a small-parameter perturbation method together with an implicit–explicit finite difference scheme. The analysis shows that the Hartmann number (Ha) largely controls the outcome of this competition. At low Ha, electroosmotic forcing dominates momentum transport, increasing flow velocity with electric field strength. At high Ha, the Lorentz force introduces electromagnetic damping that suppresses flow motion. The electric double-layer thickness regulates the spatial localization of electroosmotic forcing and significantly influences the velocity across the channel. The nonlinear rheological parameter Γ enhances electroosmotic transport through the shear-thinning response of the Powell–Eyring fluid, although this effect decreases as magnetic field strength increases. The competition between electroosmotic and electromagnetic forces also governs thermal characteristics, directly influencing both the temperature distribution and the Nusselt number Nu. The electric field enhances the convective cooling by increasing the flow velocity, whereas stronger magnetic fields suppress convection and shift heat transfer toward thermal diffusion. These findings demonstrate that the competitive interaction between electroosmotic and electromagnetic forces can be tuned through electrical, magnetic, and rheological parameters. This study provides a theoretical basis for active flow and thermal management in microfluidic devices used in biomedical and energy fields.